shows, I interlined the words above cited relating to the heavens; and, in so short and transitory an interlined hint of things, the expression of the proportion may well be excused. But if you consider the nature of the hypothesis, you will find that gravity decreases upwards, and can be no other from the superficies of the planet than reciprocally duplicate of the distance from the center, but downwards that proportion does not hold. This was but an hypothesis, and so to be looked upon only as one of my guesses, which I did not rely on; but it sufficiently explains to you why, in considering the descent of a body down to the center, I used not the duplicate proportion. In the small ascent and descent of projectiles above the earth, the variation of gravity is so inconsiderable that mathematicians neglect it. Hence the vulgar hypothesis with them is uniform gravity. And why might not I, as a mathematician, use it frequently, without thinking on the philosophy of the heavens, or believing it to be philosophically true?"67

In the body of this letter, Newton said:68 "Between ten and eleven years ago, there was an hypothesis of mine registered in your books, wherein I hinted a cause of gravity from the superficies of the planets (though for brevity's sake not there expressed) can be no other than reciprocally duplicate of the distance from the center. And I hope I shall not be urged to declare, in print, that I understood not the obvious mathematical conditions of my own hypothesis."

In a letter to Robert Boyle, which was written on February 28, 1679,69 Newton said: "I shall set down one conjecture more which came into my mind now as I was writing this letter: it is about the cause of gravity. For this end I will suppose ether to consist of parts differing

"This letter is reproduced by Brewster, op. cit., pp. 409-419. The passage given is on pp. 418-419.

from one another in subtlety, by indefinite degrees; that in the pores of bodies there is less of the grosser ether in proportion to the finer than in the regions of the air; and that yet the grosser ether in the air affects the upper regions of the earth and the finer ether in the earth the lower regions of the air, in such a manner that from the top of the air to the surface of the earth, and again from the surface of the earth to the center thereof, the ether is insensibly finer and finer. Imagine, now, any body suspended in the air or lying on the earth; the ether, being by the hypothesis grosser in the pores which are in the upper parts of the body than in those which are in its lower parts, and that grosser ether being less apt to be lodged in those pores than the finer ether below, it will endeavor to get out and give way to the finer ether below, which cannot be, without the bodies descending to make room above for it to go out into."

In this letter to Boyle, Newton deduced, from the rarification of the ether between two bodies which approach one another, firstly, an endeavor of these bodies to recede from one another, and, secondly, their adherence to one another.70

On this passage Rosenberger" remarks: "This deduction of molecular attraction and repulsion shows clearly how far Newton then was from his system of primitive or elementary forces, which only differed by the law of the actions, of all matter."

It is to be noticed that Newton himself, although he rejected the undulatory theory of light because he did not think that this theory could explain the rectilinear propagation of light, considered the whole of space to be filled with an elastic medium which propagates vibrations in a manner analogous to that in which the air propagates vibrations of sound. The ether penetrates into the pores Op. cit., p. 125.

ΤΟ

Brewster, op. cit., pp. 412-413.

71

of all material bodies, whose cohesion it brings about, it transmits gravitational action, and its irregular turbulence constitutes heat. Light, although it is not itself constituted by vibrations of this medium, but is composed of currents of corpuscles emitted by luminous bodies, freely traverses the ether. The ether has a density so small that it does not offer any sensible resistance to the heavenly bodies which move in it.72

Here may be mentioned two facts which, indirectly or directly, concern theories of ether with Newton and his predecessors.

Bullialdus derived the conclusion that the force of gravity varies inversely as the square of the distance by analogy with the diminution that occurs in the intensity of light; the opinions of Robison and Leibniz on the validity of this argument were given by Rigaud."3 The hypotheses framed by Bullialdus, Huygens, Leibniz, John Bernoulli, and Newton, to devise some mechanical cause for the effects of gravitation were also noticed by Rigaud."4

X.

About 1677, Donne and Newton visited Wren at his lodgings, and Wren "discoursed of this problem of determining the planetary motions upon philosophical principles." This was stated in a letter from Newton to Halley of May 27, 1686,75 and Newton added: "You are acquainted with Sir Christopher. Pray know where and whence he first learnt the decrease of the force in a duplicate ratio of the distance from the center."

"Cf. E. T. Whittaker, A History of the Theories of Aether and Electricity from the Age of Descartes to the Close of the Nineteenth Century, London and Dublin, 1910. Cf. also p. 534 of Mach's Mechanics.

73

74

Op. cit., p. 56.

'Op. cit., pp. 59-63, and Appendix, No. xviii, pp. 65-66, No. xx, pp. 68-70, and No. xvii, pp. 62-64 (letter to Boyle).

Halley replied to this request on June 29, 1686:76 "According to your desire in your former, I waited upon Sir Christopher Wren to inquire of him if he had the first notion of the reciprocal duplicate proportion from Mr. Hooke. His answer was that he himself, very many years since, had had his thoughts upon the making out the planets' motions by a composition of a descent towards the sun and an impressed motion; but at length he gave over, not finding the means of doing it. Since which time Mr. Hooke had frequently told him that he had done it, and attempted to make it out to him, but that he never satisfied him that his demonstrations were cogent. And this I know to be true, that in January 1683-4, I, having from the consideration of the sesquialter proportion of Kepler concluded that the centripetal force decreased in the proportion of the squares of the distances reciprocally, came one Wednesday to town, where I met with Sir Christopher Wren and Mr. Hooke, and, falling in discourse about it, Mr. Hooke affirmed that upon that principle all the laws of the celestial motions were to be demonstrated, and that he himself had done it. I declared the ill success of my attempts; and Sir Christopher, to encourage the inquiry, said that he would give Mr. Hooke or me two months' time to bring him a convincing demonstration thereof, and besides the honor, he of us that did it should have from him a present of a book of forty shillings. Mr. Hooke then said that he had it, but he would conceal it for some time that others, trying and failing, might know how to value it when he should make it public; however I remember Sir Christopher was little satisfied that he could do it, and, though Mr. Hooke then promised to show it him, I do not yet find that in that particular he has been as good as his word."

CAMBRIDGE, England.

PHILIP E. B. JOURDAIN.

"Ibid., pp. 162-163.

THE UNITS OF MEASURE AND THE PRINCIPLE

OF RELATIVITY.

"Mathematica, quae philosophiam naturalem terminare, non generare aut procreare.”—Bacon.

HE ideas which underlie scientific hypothesis, how

TH

se

ever diverse they may seem to be, rest on a common mechanical base. All phenomena are therefore explained as being due to some special form of mechanical motions of bodies, and can be reduced ultimately to modifications of inertia, velocity, momentum, or energy. These hypotheses have, in addition, this common property: they begin with the postulate of an entity which possesses inertia and velocity. Various names have been attached to this entity, but whether it be called an atom, an ether, a vortex, electricity, or energy, its function is the same. While there is little difference in the nature of this entity or substance, yet there are two diametrically opposite ways of considering its space attributes which give rise to two irreconcilable schools of thought. One of these believes the primordial substance to be discontinuous, with its parts separated by vacuous space, and the other school just as confidently maintains that there can be no empty space and that substance is continuous. Arguments for and against these two views have been unceasing and are likely to continue so long as hypothetical methods remain in vogue. The problem is quite incapable of solution because the postulate